How do I solve for x and y?

Question

asked Oct 14, 2024 127k views

1 Answer

Msrdjan · Answer 1 · 2024-10-18T09:06:04+0000

Answer:

x = 80

y = 160

Explanation:

The sum of all arc measures that make up a circle is 360°. Therefore:

$\implies 200^(\circ) + y^(\circ) = 360^(\circ)$

$\implies 200^(\circ) + y^(\circ) - 200^(\circ) = 360^(\circ) - 200^(\circ)$

$\implies y^(\circ) = 160^(\circ)$

$\implies y=160$

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:

$\implies x^(\circ)=(1)/(2) y^(\circ)$

$\implies x^(\circ)=(1)/(2) \cdot 160^(\circ)$

$\implies x^(\circ)=80^(\circ)$

$\implies x=80$

$\hrulefill$

Chord: A straight line joining two points on the circle.
Tangent: A straight line that touches a circle at only one point.
Arc: the curve between two points on the circumference of a circle
Intercepted arc: The curve between the points where two chords or line segments intercept the circumference of a circle.